One of these should do it. You will need a 16-18 vac transformer to power it up.
Ugh, link is posting as media attachment. Search Amazon for Altronix AL624.
Edir:
Nevermind. Just saw that you're charging off of 12 vdc.
Went Christmas shopping at the "fancy" mall yesterday and saw this in the Tesla showroom. It's goofy looking and the bed side panels are a bit wavy, but it's a lot bigger than I thought.